PaperlayerView exact revision on arXiv

Source-linked AI summary

Aerodynamic Prior-Free Coordinated Trajectory Generation and Tracking Control for a Tail-Sitter UAV

Erchao Rong, Zihao Liu, Junning Liang, Jianguo Wang, Xiao Jie, Haoran Fu, Ziliang Chen, Ximin Lyu

arXiv:2609.11698v1cs.RO

TL;DR

Tail-sitter control is challenged by nonlinear aerodynamics and the dependence of existing methods on airframe-specific aerodynamic identification. The paper combines an analytic ϕ-theory differential-flatness planner with reduced-model nonlinear MPC that estimates aerodynamics online, achieving high-precision tracking across tested flight regimes while retaining limitations at extreme speeds and under unmodeled conditions.

  • Problem

    Nonlinear full-envelope aerodynamics and costly, airframe-specific model identification hinder portable tail-sitter trajectory planning and tracking.

    Source: §I · p. 1

  • Method

    The framework uses a full ϕ-theory differential-flatness mapping for planning and a simplified locally valid nonlinear MPC model with online aerodynamic parameter estimation for tracking.

    Source: §I · p. 2, A. Prediction Model · p. 6

  • Results

    The framework closely tracks a high-fidelity MPC upper bound in simulation and maintains precise real-world trajectory execution across tested regimes, including peak velocity 13.3 m/s and attitudes up to 48° roll and 78° pitch.

    Source: §V · p. 7, A. Benchmark under Various Aerodynamic… · p. 8, 2) Typical Maneuvers in Field… · p. 9

  • Takeaways & Limitations

    The method can be adapted across configurations and used as an initial controller for collecting flight data without airframe-specific aerodynamic priors.

    Source: §VI · pp. 10–11

Abstract

from arXiv · show

This paper presents a coordinated trajectory generation and tracking control framework for a tail-sitter unmanned aerial vehicle (UAV), which does not require aerodynamic priors identified for a specific airframe while addressing the challenge of flight control under highly nonlinear aerodynamics across the full flight envelope. The core innovation lies in employing phase-specific aerodynamic modeling strategies for planning and tracking, tailored to their distinct functional characteristics, without requiring airframe-specific aerodynamic priors. Specifically, the phi-theory model under coordinated flight is employed to derive an analytic differential flatness mapping, and a simplified but locally accurate model is established for predictive control to enable real-time aerodynamic parameter estimation. The proposed framework is evaluated extensively through both simulation and challenging real-world flight tests under mild wind conditions, showing high-precision tracking and adaptability across the tested aerodynamic conditions. To the best of our knowledge, this is the first real-world demonstration of accurate trajectory tracking over tested flight regimes spanning the full envelope of a tail-sitter UAV without relying on aerodynamic identification campaigns. The source code of our framework is available at: https://github.com/SYSU-HILAB/AP-PnC.

I. INTRODUCTION

Tail-sitter flight control is difficult because large attitude shifts create strongly varying, nonlinear aerodynamics, while existing high-performance approaches depend on airframe-specific aerodynamic models. The paper introduces an integrated framework combining analytic trajectory generation and adaptive predictive control without costly aerodynamic identification.

I. INTRODUCTION

  • Prior high-performance tail-sitter controllers rely on high-fidelity aerodynamic models, creating portability, hardware, and computational challenges.The paper positions its approach against model-dependent tracking and planning methods whose predictive performance requires advance aerodynamic characterization.Source: §I · pp. 1–2
  • The framework addresses nonlinear full-envelope control without requiring airframe-specific aerodynamic identification.It targets portability and reduced deployment cost while retaining coordinated trajectory planning and tracking.Source: §I · pp. 1–2
  • An analytic differential-flatness mapping based on the full ϕ-theory model generates feasible trajectories and reference states without advance aerodynamic characterization.The mapping uses coordinated-flight dynamics and aerodynamic force relations to avoid explicit dynamic integration during planning.Source: §I · p. 2
  • A nonlinear MPC estimates and adapts to aerodynamic characteristics online, avoiding costly model-identification campaigns during deployment.The controller is designed to replace extensive aerodynamic estimation setups and resource-intensive identification procedures.Source: §I · pp. 1–2
  • The paper reports sub-meter position RMSE over tested flight regimes without an aerodynamic identification campaign and provides open-source code for further validation.The framework is evaluated through simulation and experiments, with the source code released for community investigation.Source: §I · p. 2

B. Kinematics

The vehicle kinematics describe translational and rotational motion using position derivatives, proper acceleration, angular velocity, inertia, and applied moments. Aerodynamic force, thrust, and thrust-moment models are handled differently in planning and tracking.

B. Kinematics

  • Proper acceleration is defined as the acceleration excluding gravity and is produced by thrust and aerodynamic forces.The translational model uses proper acceleration to connect vehicle motion with force generation.Source: B. Kinematics · p. 3
  • The rotational dynamics use the aircraft inertia matrix, body-frame angular velocity, and total moment from aerodynamic and thrust moments.The cross-product operator represents vector products in the rotational equations.Source: B. Kinematics · p. 3
  • The nominal system state is defined before separating aerodynamic-force, thrust, and thrust-moment modeling across planning and tracking.Aerodynamic moment is treated as a disturbance and compensated by a low-level controller.Source: B. Kinematics · p. 3

C. System Framework

The framework uses phase-specific aerodynamic models: a feasibility-oriented full-envelope model for long-horizon planning and a locally valid reduced model for short-horizon MPC tracking. It assumes wind-free coordinated flight and estimates a dominant aerodynamic parameter online.

C. System Framework

  • Planning uses differential flatness with the ϕ-theory model, while tracking uses a locally valid simplified model for real-time aerodynamic adaptation.The two models are deliberately tailored to long-horizon trajectory generation and short-horizon predictive control.Source: C. System Framework · p. 3, §III · p. 4, A. Differential Flatness · p. 4
  • The tracking model retains one online-estimated longitudinal aerodynamic parameter while treating other effects through low-level compensation or coordination assumptions.The implementation preserves Bcz, treats Bcx as a matched disturbance, assumes Bcy vanishes under coordination, and neglects aerodynamic moment.Source: C. System Framework · p. 3
  • The planner generates a dynamically feasible trajectory offline, extracts position, velocity, and lateral-axis references, and supplies them to online MPC.MPC solves a receding-horizon optimization using augmented state estimates and sends predicted angular velocity and proper acceleration to the low-level controller.Source: C. System Framework · p. 3
  • The framework assumes wind-free conditions and coordinated flight, with sustained sideslip maneuvers outside its design scope.Wind is excluded as an aerodynamic disturbance, and lateral-axis tracking is used to suppress sideslip.Source: C. System Framework · pp. 3–4
  • Under coordinated flight, differential flatness uses position as the flat output and expresses relevant states and inputs through position derivatives up to third order.The stability-frame kinematic structure and ϕ-theory force relations close the dynamics-dependent portion of the flatness map.Source: 1) Coordinated Flight Model · p. 4, A. Differential Flatness · p. 4

2) ϕ-theory Model:

The ϕ-theory model provides an analytic differential-flatness mapping for coordinated tail-sitter flight, allowing attitude, thrust, and angular velocity references to be derived from position trajectories. Restricting the planning model to ϕ33 enables aerodynamic-prior-free trajectory generation.

ϕ-theory Model:

  • The full-flight-envelope mapping requires an aerodynamic model for angle of attack, obtained by decomposing the dynamics in the longitudinal plane.The longitudinal decomposition relates aerodynamic and proper accelerations through angle of attack.Source: 2) ϕ-theory Model · p. 4
  • The ϕ-theory model avoids generally unavailable closed-form solutions for complex aerodynamic maps by expressing aerodynamic force through ϕ coefficients.Each ϕ coefficient is mass-normalized, and the mass converts modeled aerodynamic acceleration to force.Source: 2) ϕ-theory Model · p. 4
  • ϕ-theory analytically solves angle of attack, enabling computation of attitude and thrust from the modeled aerodynamic force.The resulting body-frame attitude is determined from the rotation between frames, while thrust acceleration is assumed aligned with xb.Source: 2) ϕ-theory Model · p. 4
  • The differential-flatness mapping additionally derives body-frame angular velocity by differentiating the attitude relation and incorporating trajectory jerk.Determining angular velocity requires the time derivative of angle of attack.Source: 2) ϕ-theory Model · pp. 4–5
  • For planning, the model retains only ϕ33 = 0.5ρSCD,flat/m, equivalent to ignoring the axial aerodynamic coefficient Bcx.This restriction defines the aerodynamic prior-free planner using air density, wing area, and flat-plate drag coefficient terms.Source: 2) ϕ-theory Model · p. 5

B. Spatial-temporal Trajectory Generation

The planner represents trajectories as piecewise seventh-order polynomial splines parameterized by intermediate waypoints and segment times. GCOPTER and TMINCO optimize these variables while enforcing dynamic feasibility through differential-flatness propagation and penalized constraints.

B. Spatial-temporal Trajectory Generation

  • TMINCO parameterizes the trajectory with intermediate waypoints Q and segment durations T, producing piecewise polynomial coefficients.The trajectory contains M segments, with waypoint and time-allocation variables optimized from fixed initial and terminal positions.Source: B. Spatial-temporal Trajectory… · p. 5
  • Seventh-order polynomial splines provide C3 continuity across the complete trajectory.The polynomial basis is β(s) = (1, s, . . . , s7).Source: B. Spatial-temporal Trajectory… · p. 5
  • The planner iteratively evaluates TMINCO trajectories, applies differential-flatness propagation, updates variables by line search, and returns the optimized trajectory.The algorithm initializes waypoints and time allocation, uses L-BFGS updates, and terminates when the gradient norm falls below the specified threshold.Source: B. Spatial-temporal Trajectory… · p. 5
  • GCOPTER converts waypoint, timing, velocity, angular-velocity, and acceleration requirements into an unconstrained nonlinear program.Constraint violations are incorporated into the cost using a quadratic exterior penalty method.Source: B. Spatial-temporal Trajectory… · pp. 5–6
  • Differential-flatness backpropagation computes constraint gradients along uniformly sampled trajectories and propagates them to waypoint and timing variables.Forward-mode automatic differentiation avoids cumbersome symbolic derivation of the flatness-map gradient.Source: B. Spatial-temporal Trajectory… · p. 6

IV. TRAJECTORY TRACKING CONTROL

The proposed aerodynamic prior-free MPC tracks coordinated-flight trajectories using online aerodynamic-parameter estimation. This enables high-accuracy tracking without requiring airframe-specific aerodynamic characterization in advance.

IV. TRAJECTORY TRACKING CONTROL

  • The aerodynamic prior-free MPC incorporates an online estimated aerodynamic parameter to achieve high-accuracy tracking of coordinated-flight trajectories.The controller is developed under the paper’s phase-specific modeling strategy for tracking control.Source: §IV · p. 6

A. Prediction Model

The prediction model retains the dominant axial aerodynamic effect while simplifying lateral coefficients and aerodynamic moments. Treating the retained coefficient as a time-varying augmented state enables locally valid adaptive prediction over the full flight envelope.

A. Prediction Model

  • Bcz is augmented into the nominal state and estimated online, allowing adaptive control over the MPC’s short prediction horizon.The parameter is modeled as time-varying because local validity over short horizons is sufficient for MPC.Source: A. Prediction Model · p. 6
  • The aerodynamic parameter dynamics encode the typical relation between pitch motion and the magnitude of the axial aerodynamic effect.Pitch down typically decreases its magnitude, whereas pitch up typically increases it.Source: A. Prediction Model · p. 6
  • The MPC augments the state with the four actuator thrust forces so generated control force and moment can be constrained.The input is defined through thrust-force rates for the four motors.Source: A. Prediction Model · p. 6
  • The retained prediction model is locally valid across the full flight envelope while preserving the most significant aerodynamic effect from the controller’s perspective.This modeling choice supports adaptive tracking without requiring a globally accurate aerodynamic model.Source: A. Prediction Model · p. 6

B. MPC Optimization Problem Formulation

The MPC predicts coordinated-flight dynamics while integrating trajectory tracking, control effort, and coordinated-flight costs under actuator and command-bandwidth constraints.

C. Augmented State Estimation

The augmented-state estimator focuses on aerodynamic thrust and drag-related components without requiring motor-speed sensing or a pre-identified propeller model.

  • The estimator obtains nominal position, velocity, attitude, and angular-rate states from a standard estimator while focusing on thrust force and aerodynamic parameter components.Source: C. Augmented State Estimation · p. 7
  • The thrust force is initialized from the previous MPC result instead of motor-speed measurements, avoiding extra hardware and a pre-identified propeller model.Source: C. Augmented State Estimation · p. 7
  • The aerodynamic parameter is estimated from filtered acceleration measurements with a denominator offset and clamping to prevent singularities and over-estimation.Source: C. Augmented State Estimation · p. 7

V. EXPERIMENTS

Simulation and field experiments evaluate the aerodynamic prior-free framework across tracking tasks and aggressive transitions, including peak velocity of 13.3 m/s and large roll and pitch angles.

  • The framework maintains precise trajectory execution without aerodynamic priors during aggressive tests reaching 13.3 m/s, 48° roll, and 78° pitch.Source: §V · p. 7

A. Benchmark under Various Aerodynamic Conditions

The benchmark compares the proposed controller with prior-based baselines across aerodynamic models and flight regimes, showing near-upper-bound RMSE but larger high-speed worst-case errors and wind-sensitive limits.

C. Field Experiments

Field experiments validate coordinated circular, ∞-shaped, and rapid-transition flights without airframe-specific aerodynamic priors, including aggressive maneuvers and tested wind conditions.

Typical Maneuvers in Field Environments

  • 0.39 m circular-flight position RMSE and 0.42 m ∞-shaped-flight average error demonstrate precise trajectory tracking across three-phase maneuvers.Both trajectories include forward transition, level flight, and backward transition; the circular trajectory reaches 0.66 m MaxAE, while the ∞-shaped trajectory reaches 0.73 m.Source: 2) Typical Maneuvers in Field… · p. 9, Figure 7 · p. 10, Figure 8 · p. 10
  • The vehicle closely tracks position, velocity, and lateral-axis references despite no aerodynamic priors and maximum tilt exceeding 80°.During level flight, the ground-velocity-based sideslip proxy remains within 10° for nearly the entire duration of both trajectories.Source: 2) Typical Maneuvers in Field… · pp. 9–10

Fast Transitions

  • 0.54 m forward and 0.25 m backward height MaxAE outperform the baseline’s 1.15 m and 1.00 m during the most aggressive transitions.The comparison uses the same low-level controller, while the baseline relies on aerodynamic priors and altitude regulation.Source: 3) Fast Transitions · p. 10, Figure 9 · p. 11

Conclusion and Future Work

  • The framework is presented as adaptable across configurations and suitable for deployment without airframe-specific aerodynamic priors.The authors also describe it as a potential initial controller for collecting flight data for later high-fidelity model-based design.Source: §VI · pp. 10–11
  • Under tested wind disturbances, MaxAE remains at or below 1 m in moderate tailwinds but degrades under mild headwind and crosswind.The worst degradation occurs under combined headwind and crosswind when low-AoA high-stiffness behavior coincides with violation of the coordinated-flight constraint.Source: §VI · p. 11

Related papers

Loading 2609.11698v1…